Problem: Solve for $y$, $ -\dfrac{9}{y + 5} = \dfrac{5}{4y + 20} - \dfrac{4y - 3}{5y + 25} $
Explanation: First we need to find a common denominator for all the expressions. This means finding the least common multiple of $y + 5$ $4y + 20$ and $5y + 25$ The common denominator is $20y + 100$ To get $20y + 100$ in the denominator of the first term, multiply it by $\frac{20}{20}$ $ -\dfrac{9}{y + 5} \times \dfrac{20}{20} = -\dfrac{180}{20y + 100} $ To get $20y + 100$ in the denominator of the second term, multiply it by $\frac{5}{5}$ $ \dfrac{5}{4y + 20} \times \dfrac{5}{5} = \dfrac{25}{20y + 100} $ To get $20y + 100$ in the denominator of the third term, multiply it by $\frac{4}{4}$ $ -\dfrac{4y - 3}{5y + 25} \times \dfrac{4}{4} = -\dfrac{16y - 12}{20y + 100} $ This give us: $ -\dfrac{180}{20y + 100} = \dfrac{25}{20y + 100} - \dfrac{16y - 12}{20y + 100} $ If we multiply both sides of the equation by $20y + 100$ , we get: $ -180 = 25 - 16y + 12$ $ -180 = -16y + 37$ $ -217 = -16y $ $ y = \dfrac{217}{16}$